Finite Group Databasebeta

← C43×#19518 #24939535

Subgroups — C43×#19518 #24939535

Order 11008.

580 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3254C211yesmaximal, characteristic
2C43×#3246C211yesmaximal, characteristic
3C43×#3231C211yesmaximal, characteristic, complemented
4C43×#2981C211yesmaximal, characteristic
5C43×#1699C212yesmaximal, complemented
6C43×#1691C212yesmaximal, complemented
7C43×#1683C212yesmaximal, complemented
8C43×#1673C212yesmaximal, complemented
9C43×#1571C211yesmaximal, characteristic, complemented
10C43×#1559C211yesmaximal, characteristic, complemented
11C43×#1552C211yesmaximal, characteristic, complemented
12C43×#533C2211yescharacteristic
13C43×#533C2211yescharacteristic
14C43×#532C2211yescharacteristic
15C43×#500C2211yescharacteristic
16C43×#498C2211yescharacteristic
17C43×#487C2211yescharacteristic
18C43×#487C2211yescharacteristic
19C43×#485—22no—
20C43×#479—22no—
21C43×#477—21no—
22C43×#476C2212yes—
23C43×#475—21no—
24C43×#474C2212yes—
25C43×#468—22no—
26C43×#465—22no—
27C43×#461C2212yes—
28C43×#461C2212yes—
29C43×#460—21no—
30C43×#460—21no—
31C43×#436C2212yes—
32C43×#435—22no—
33C8×D4×C43C2212yes—
34C43×#432C2211yescharacteristic
35C43×#431C2211yescharacteristic
36C43×#423C2211yescharacteristic
37C2×C4⋊C8×C43C2211yescharacteristic
38C43×#408—22no—
39C43×#335C2212yes—
40C43×#335C2212yes—
41C43×#333C2212yes—
42C43×#332C2212yes—
43C43×#332C2212yes—
44C43×#332C2212yes—
45C2×#41×C43—21no—
46C2×SD16×C43—22no—
47C2×SD16×C43—22no—
48C2×M16×C43—21no—
49C2×M16×C43—22no—
50C22×C8×C43—21no—
51C22×C8×C43—22no—
52C4⋊Q8×C43D411yescharacteristic
53C4⋊Q8×C43C2311yescharacteristic
54C4⋊Q8×C43C2311yescharacteristic
55C4⋊Q8×C43C2311yescharacteristic
56C4⋊Q8×C43C2311yescharacteristic
57#127×C43D411yescharacteristic
58#125×C43—21no—
59#125×C43—21no—
60#124×C43—21no—
61C22⋊Q8×C43—21no—
62C22⋊Q8×C43—21no—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65#121×C43—21no—
66#121×C43D412yes—
67C4×Q8×C43—21no—
68C4×Q8×C43—21no—
69C4×Q8×C43—21no—
70C4×Q8×C43—21no—
71C4×D4×C43—21no—
72C4×D4×C43C2312yes—
73#117×C43—21no—
74#117×C43—21no—
75C2×C42×C43C2311yescharacteristic
76#107×C43—22no—
77#107×C43—22no—
78#106×C43—22no—
79#106×C43—22no—
80C4⋊C8×C43—21no—
81C4⋊C8×C43—21no—
82C4⋊C8×C43D412yes—
83C4⋊C8×C43C2312yes—
84C4⋊C8×C43C2312yes—
85C4⋊C8×C43C2312yes—
86#103×C43—22no—
87#103×C43—22no—
88#103×C43—22no—
89#103×C43—22no—
90#102×C43—22no—
91#102×C43—22no—
92C22⋊C8×C43—21no—
93C22⋊C8×C43—22no—
94C22⋊C8×C43—22no—
95C22⋊C8×C43D412yes—
96#97×C43—21no—
97C4×C8×C43C2311yescharacteristic
98C4×C8×C43C2311yescharacteristic
99#41×C43—82no—
100C2×Q8×C43—21no—
101C2×Q8×C43—21no—
102C2×Q8×C43—21no—
103C2×Q8×C43—21no—
104C2×Q8×C43—21no—
105C2×D4×C43—21no—
106C2×D4×C43—21no—
107C2×D4×C43—22no—
108C2×D4×C43C2×D412yes—
109C22×C4×C43—22no—
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43#4111yescharacteristic
113SD16×C43—82no—
114SD16×C43—82no—
115M16×C43—82no—
116M16×C43—81no—
117C2×C8×C43—22no—
118C2×C8×C43—22no—
119C2×C8×C43—22no—
120C2×C8×C43—82no—
121C2×C8×C43—81no—
122C2×C8×C43C2×D412yes—
123C2×C8×C43C2×D412yes—
124C4⋊C4×C43—21no—
125C4⋊C4×C43—21no—
126C4⋊C4×C43—21no—
127C4⋊C4×C43—21no—
128C4⋊C4×C43—21no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—41no—
134C4⋊C4×C43—41no—
135C4⋊C4×C43—41no—
136C4⋊C4×C43—41no—
137C4⋊C4×C43C2×D412yes—
138C22⋊C4×C43—22no—
139C22⋊C4×C43—22no—
140C22⋊C4×C43—41no—
141C22⋊C4×C43—41no—
142C42×C43—41no—
143C42×C43—41no—
144C42×C43C2×D411yescharacteristic
145C42×C43C2×D411yescharacteristic
146C42×C43#4111yescharacteristic
147C42×C43C2411yescharacteristic
148C23×C43—22no—
149C23×C43#12111yescharacteristic
150Q8×C43—41no—
151Q8×C43—41no—
152Q8×C43—42no—
153Q8×C43—41no—
154Q8×C43—41no—
155Q8×C43—81no—
156Q8×C43—81no—
157D4×C43—22no—
158D4×C43—22no—
159D4×C43—81no—
160D4×C43—81no—
161D4×C43—82no—
162C2×C4×C43—21no—
163C2×C4×C43—22no—
164C2×C4×C43—21no—
165C2×C4×C43—22no—
166C2×C4×C43—41no—
167C2×C4×C43—42no—
168C2×C4×C43—42no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43#12111yescharacteristic
174C2×C4×C43#12111yescharacteristic
175C2×C4×C43#12111yescharacteristic
176C2×C4×C43C22×D411yescharacteristic
177C2×C4×C43C22×D411yescharacteristic
178C2×C4×C43C2×#4111yescharacteristic
179C8×C43—22no—
180C8×C43—22no—
181C8×C43—42no—
182C8×C43—42no—
183C8×C43—42no—
184#19518C4311yesmaximal, characteristic, direct product factor, Sylow
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—42no—
189C22×C43—42no—
190C22×C43—42no—
191C22×C43C2×#12111yescharacteristic
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—42no—
197C4×C43—81no—
198C4×C43—81no—
199C4×C43—81no—
200C4×C43—81no—
201C4×C43#57611yescharacteristic
202C4×C43#57712yes—
203C4×C43#57811yescharacteristic
204#3254C2×C4311yescharacteristic
205#3246C2×C4311yescharacteristic
206#3231C2×C4311yescharacteristic, complemented
207#2981C2×C4311yescharacteristic
208#1699C2×C4312yescomplemented
209#1691C2×C4312yescomplemented
210#1683C2×C4312yescomplemented
211#1673C2×C4312yescomplemented
212#1571C2×C4311yescharacteristic, complemented
213#1559C2×C4311yescharacteristic, complemented
214#1552C2×C4311yescharacteristic, complemented
215C2×C43—41no—
216C2×C43—82no—
217C2×C43#304211yescharacteristic
218C2×C43#306111yescharacteristic
219C2×C43#306911yescharacteristic
220#533C22×C4311yescharacteristic
221#533C22×C4311yescharacteristic
222#532C22×C4311yescharacteristic
223#500C22×C4311yescharacteristic
224#498C22×C4311yescharacteristic
225#487C22×C4311yescharacteristic
226#487C22×C4311yescharacteristic
227#485—22no—
228#479—22no—
229#477—21no—
230#476C22×C4312yes—
231#475—21no—
232#474C22×C4312yes—
233#468—22no—
234#465—22no—
235#461C22×C4312yes—
236#461C22×C4312yes—
237#460—21no—
238#460—21no—
239#436C22×C4312yes—
240#435—22no—
241C8×D4C22×C4312yes—
242#432C22×C4311yescharacteristic
243#431C22×C4311yescharacteristic
244#423C22×C4311yescharacteristic
245C2×C4⋊C8C22×C4311yescharacteristic
246#408—22no—
247#335C22×C4312yes—
248#335C22×C4312yes—
249#333C22×C4312yes—
250#332C22×C4312yes—
251#332C22×C4312yes—
252#332C22×C4312yes—
253C43#1951811yescharacteristic, direct product factor, Sylow
254C2×#41—21no—
255C2×SD16—22no—
256C2×SD16—22no—
257C2×M16—21no—
258C2×M16—22no—
259C22×C8—21no—
260C22×C8—22no—
261C4⋊Q8D4×C4311yescharacteristic
262C4⋊Q8C23×C4311yescharacteristic
263C4⋊Q8C23×C4311yescharacteristic
264C4⋊Q8C23×C4311yescharacteristic
265C4⋊Q8C23×C4311yescharacteristic
266#127D4×C4311yescharacteristic
267#125—21no—
268#125—21no—
269#124—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273C22⋊Q8—21no—
274#121—21no—
275#121D4×C4312yes—
276C4×Q8—21no—
277C4×Q8—21no—
278C4×Q8—21no—
279C4×Q8—21no—
280C4×D4—21no—
281C4×D4C23×C4312yes—
282#117—21no—
283#117—21no—
284C2×C42C23×C4311yescharacteristic
285#107—22no—
286#107—22no—
287#106—22no—
288#106—22no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8D4×C4312yes—
292C4⋊C8C23×C4312yes—
293C4⋊C8C23×C4312yes—
294C4⋊C8C23×C4312yes—
295#103—22no—
296#103—22no—
297#103—22no—
298#103—22no—
299#102—22no—
300#102—22no—
301C22⋊C8—21no—
302C22⋊C8—22no—
303C22⋊C8—22no—
304C22⋊C8D4×C4312yes—
305#97—21no—
306C4×C8C23×C4311yescharacteristic
307C4×C8C23×C4311yescharacteristic
308#41—82no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×D4—22no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4C2×D4×C4312yes—
318C22×C4—22no—
319C22×C4C2×D4×C4311yescharacteristic
320C22×C4C2×D4×C4311yescharacteristic
321C22×C4#41×C4311yescharacteristic
322SD16—82no—
323SD16—82no—
324M16—82no—
325M16—81no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—82no—
330C2×C8—81no—
331C2×C8C2×D4×C4312yes—
332C2×C8C2×D4×C4312yes—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4C2×D4×C4312yes—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C42—41no—
352C42—41no—
353C42C2×D4×C4311yescharacteristic
354C42C2×D4×C4311yescharacteristic
355C42#41×C4311yescharacteristic
356C42C24×C4311yescharacteristic
357C23—22no—
358C23#121×C4311yescharacteristic
359Q8—41no—
360Q8—41no—
361Q8—42no—
362Q8—41no—
363Q8—41no—
364Q8—81no—
365Q8—81no—
366D4—22no—
367D4—22no—
368D4—81no—
369D4—81no—
370D4—82no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4#121×C4311yescharacteristic
383C2×C4#121×C4311yescharacteristic
384C2×C4#121×C4311yescharacteristic
385C2×C4C22×D4×C4311yescharacteristic
386C2×C4C22×D4×C4311yescharacteristic
387C2×C4C2×#41×C4311yescharacteristic
388C8—22no—
389C8—22no—
390C8—42no—
391C8—42no—
392C8—42no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—42no—
397C22—42no—
398C22—42no—
399C22C2×#121×C4311yescharacteristic
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—42no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4C43×#57611yescharacteristic
410C4C43×#57712yes—
411C4C43×#57811yescharacteristic
412C2—41no—
413C2—82no—
414C2C43×#304211yescharacteristic
415C2C43×#306111yescharacteristic
416C2C43×#306911yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C43×#3231C2semidirect
5. C43×#1699C2semidirect
6. C43×#1691C2semidirect
7. C43×#1683C2semidirect
8. C43×#1673C2semidirect
9. C43×#1571C2semidirect
10. C43×#1559C2semidirect
11. C43×#1552C2semidirect
184. #19518C43direct (N × H)
206. #3231C2×C43semidirect
208. #1699C2×C43semidirect
209. #1691C2×C43semidirect
210. #1683C2×C43semidirect
211. #1673C2×C43semidirect
212. #1571C2×C43semidirect
213. #1559C2×C43semidirect
214. #1552C2×C43semidirect
253. C43#19518direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C43×#32542
C43×#32462
C43×#32312
C43×#29812
C43×#16992
C43×#16912
C43×#16832
C43×#16732
C43×#15712
C43×#15592
C43×#15522
#1951843